Precalculus Examples

$| x - 19 | = - (x - 19)$

Step 1

Simplify $- (x - 19)$ .

Tap for more steps...

Step 1.1

Apply the distributive property.

$| x - 19 | = - x - - 19$

Step 1.2

Multiply $- 1$ by $- 19$ .

$| x - 19 | = - x + 19$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 50, - 49.7, - 49.6, - 49.3, - 49.2, - 48.9, - 48.8, - 48.5, - 48.4, - 48.1, - 48, - 47.7, - 47.6, - 47.3, - 47.2, - 47.1, - 47, - 46.9, - 46.8, - 46.5, - 46.3\overline{9}, - 46.0\overline{9}, - 46, - 45.6\overline{9}, - 45.5\overline{9}, - 45.2\overline{9}, - 45.1\overline{9}, - 32, - 31.8\overline{9}, - 31.7\overline{9}, - 31.6\overline{9}, - 31.5\overline{9}, - 31.4\overline{9}, - 31.3\overline{9}, - 31.2\overline{9}, - 31.1\overline{9}, - 31.0\overline{9}, - 31, - 30.8\overline{9}, - 30.7\overline{9}, - 30.4\overline{9}, - 30.1\overline{9}, - 30.0\overline{9}, - 30, - 29.8\overline{9}, - 29.7\overline{9}, - 29.6\overline{9}, - 29.5\overline{9}, - 29.4\overline{9}, - 29.3\overline{9}, - 29.2\overline{9}, - 29.1\overline{9}, - 29.0\overline{9}, - 28.7\overline{9}, - 28.6\overline{9}, - 28.5\overline{9}, - 28.4\overline{9}, - 28.3\overline{9}, - 28.2\overline{9}, - 28.1\overline{9}, - 28.0\overline{9}, - 28, - 27.8\overline{9}, - 27.7\overline{9}, - 27.6\overline{9}, - 27.3\overline{9}, - 27.2\overline{9}, - 27.1\overline{9}, - 27.0\overline{9}, - 27, - 26.8\overline{9}, - 26.7\overline{9}, - 26.6\overline{9}, - 26.5\overline{9}, - 26.4\overline{9}, - 26.3\overline{9}, - 26.2\overline{9}, - 26.1\overline{9}, - 26.0\overline{9}, - 26, - 25.8\overline{9}, - 25.7\overline{9}, - 25.6\overline{9}, - 25.3\overline{9}, - 25.2\overline{9}, - 25.1\overline{9}, - 25.0\overline{9}, - 25, - 24.8\overline{9}, - 24.7\overline{9}, - 24.6\overline{9}, - 24.5\overline{9}, - 24.2\overline{9}, - 24.1\overline{9}, - 24.0\overline{9}, - 24, - 23.8\overline{9}, - 23.7\overline{9}, - 23.6\overline{9}, - 23.5\overline{9}, - 23.4\overline{9}, - 23.3\overline{9}, - 23.2\overline{9}, - 23.1\overline{9}, - 23.0\overline{9}, - 23, - 22.8\overline{9}, - 22.5\overline{9}, - 22.4\overline{9}, - 22.3\overline{9}, - 22.2\overline{9}, - 22.1\overline{9}, - 22.0\overline{9}, - 22, - 21.8\overline{9}, - 21.7\overline{9}, - 21.4\overline{9}, - 21.1\overline{9}, - 21.0\overline{9}, - 21, - 20.8\overline{9}, - 20.7\overline{9}, - 20.6\overline{9}, - 20.5\overline{9}, - 20.4\overline{9}, - 20.3\overline{9}, - 20.2\overline{9}, - 20.1\overline{9}, - 20.0\overline{9}, - 20, - 19.8\overline{9}, - 19.7\overline{9}, - 19.6\overline{9}, - 19.5\overline{9}, - 19.4\overline{9}, - 19.1\overline{9}, - 19.0\overline{9}, - 19, - 18.8\overline{9}, - 18.7\overline{9}, - 18.6\overline{9}, - 18.5\overline{9}, - 18.4\overline{9}, - 18.3\overline{9}, - 18.2\overline{9}, - 18.1\overline{9}, - 18.0\overline{9}, - 18, - 17.8\overline{9}, - 17.7\overline{9}, - 17.6\overline{9}, - 17.5\overline{9}, - \frac{35}{2}, - 17.3\overline{9}, - 17.2\overline{9}, - 17.1\overline{9}, - 17.0\overline{9}, - 17, - 16.8\overline{9}, - 16.7\overline{9}, - 16.6\overline{9}, - 16.5\overline{9}, - \frac{33}{2}, - 16.3\overline{9}, - 16.2\overline{9}, - 16.1\overline{9}, - 16.0\overline{9}, - 16, - 15.8\overline{9}, - 15.6\overline{9}, - 15.5\overline{9}, - \frac{31}{2}, - 15.3\overline{9}, - 15.0\overline{9}, - 15, - 14.7\overline{9}, - 14.6\overline{9}, - 14.5\overline{9}, - 14.2\overline{9}, - 14.1\overline{9}, - 14.0\overline{9}, - 14, - 13.8\overline{9}, - 13.7\overline{9}, - 13.6\overline{9}, - \frac{27}{2}, - 13.3\overline{9}, - 13.2\overline{9}, - 13.1\overline{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

$x \approx - 50, - 49.7, - 49.6, - 49.3, - 49.2, - 48.9, - 48.8, - 48.5, - 48.4, - 48.1, - 48, - 47.7, - 47.6, - 47.3, - 47.2, - 47.1, - 47, - 46.9, - 46.8, - 46.5, - 46.3\overline{9}, - 46.0\overline{9}, - 46, - 45.6\overline{9}, - 45.5\overline{9}, - 45.2\overline{9}, - 45.1\overline{9}, - 32, - 31.8\overline{9}, - 31.7\overline{9}, - 31.6\overline{9}, - 31.5\overline{9}, - 31.4\overline{9}, - 31.3\overline{9}, - 31.2\overline{9}, - 31.1\overline{9}, - 31.0\overline{9}, - 31, - 30.8\overline{9}, - 30.7\overline{9}, - 30.4\overline{9}, - 30.1\overline{9}, - 30.0\overline{9}, - 30, - 29.8\overline{9}, - 29.7\overline{9}, - 29.6\overline{9}, - 29.5\overline{9}, - 29.4\overline{9}, - 29.3\overline{9}, - 29.2\overline{9}, - 29.1\overline{9}, - 29.0\overline{9}, - 28.7\overline{9}, - 28.6\overline{9}, - 28.5\overline{9}, - 28.4\overline{9}, - 28.3\overline{9}, - 28.2\overline{9}, - 28.1\overline{9}, - 28.0\overline{9}, - 28, - 27.8\overline{9}, - 27.7\overline{9}, - 27.6\overline{9}, - 27.3\overline{9}, - 27.2\overline{9}, - 27.1\overline{9}, - 27.0\overline{9}, - 27, - 26.8\overline{9}, - 26.7\overline{9}, - 26.6\overline{9}, - 26.5\overline{9}, - 26.4\overline{9}, - 26.3\overline{9}, - 26.2\overline{9}, - 26.1\overline{9}, - 26.0\overline{9}, - 26, - 25.8\overline{9}, - 25.7\overline{9}, - 25.6\overline{9}, - 25.3\overline{9}, - 25.2\overline{9}, - 25.1\overline{9}, - 25.0\overline{9}, - 25, - 24.8\overline{9}, - 24.7\overline{9}, - 24.6\overline{9}, - 24.5\overline{9}, - 24.2\overline{9}, - 24.1\overline{9}, - 24.0\overline{9}, - 24, - 23.8\overline{9}, - 23.7\overline{9}, - 23.6\overline{9}, - 23.5\overline{9}, - 23.4\overline{9}, - 23.3\overline{9}, - 23.2\overline{9}, - 23.1\overline{9}, - 23.0\overline{9}, - 23, - 22.8\overline{9}, - 22.5\overline{9}, - 22.4\overline{9}, - 22.3\overline{9}, - 22.2\overline{9}, - 22.1\overline{9}, - 22.0\overline{9}, - 22, - 21.8\overline{9}, - 21.7\overline{9}, - 21.4\overline{9}, - 21.1\overline{9}, - 21.0\overline{9}, - 21, - 20.8\overline{9}, - 20.7\overline{9}, - 20.6\overline{9}, - 20.5\overline{9}, - 20.4\overline{9}, - 20.3\overline{9}, - 20.2\overline{9}, - 20.1\overline{9}, - 20.0\overline{9}, - 20, - 19.8\overline{9}, - 19.7\overline{9}, - 19.6\overline{9}, - 19.5\overline{9}, - 19.4\overline{9}, - 19.1\overline{9}, - 19.0\overline{9}, - 19, - 18.8\overline{9}, - 18.7\overline{9}, - 18.6\overline{9}, - 18.5\overline{9}, - 18.4\overline{9}, - 18.3\overline{9}, - 18.2\overline{9}, - 18.1\overline{9}, - 18.0\overline{9}, - 18, - 17.8\overline{9}, - 17.7\overline{9}, - 17.6\overline{9}, - 17.5\overline{9}, - 17.5, - 17.3\overline{9}, - 17.2\overline{9}, - 17.1\overline{9}, - 17.0\overline{9}, - 17, - 16.8\overline{9}, - 16.7\overline{9}, - 16.6\overline{9}, - 16.5\overline{9}, - 16.5, - 16.3\overline{9}, - 16.2\overline{9}, - 16.1\overline{9}, - 16.0\overline{9}, - 16, - 15.8\overline{9}, - 15.6\overline{9}, - 15.5\overline{9}, - 15.5, - 15.3\overline{9}, - 15.0\overline{9}, - 15, - 14.7\overline{9}, - 14.6\overline{9}, - 14.5\overline{9}, - 14.2\overline{9}, - 14.1\overline{9}, - 14.0\overline{9}, - 14, - 13.8\overline{9}, - 13.7\overline{9}, - 13.6\overline{9}, - 13.5, - 13.3\overline{9}, - 13.2\overline{9}, - 13.1\overline{9}$

Mixed Number Form:

$x \approx - 50, - 49.7, - 49.6, - 49.3, - 49.2, - 48.9, - 48.8, - 48.5, - 48.4, - 48.1, - 48, - 47.7, - 47.6, - 47.3, - 47.2, - 47.1, - 47, - 46.9, - 46.8, - 46.5, - 46.3\overline{9}, - 46.0\overline{9}, - 46, - 45.6\overline{9}, - 45.5\overline{9}, - 45.2\overline{9}, - 45.1\overline{9}, - 32, - 31.8\overline{9}, - 31.7\overline{9}, - 31.6\overline{9}, - 31.5\overline{9}, - 31.4\overline{9}, - 31.3\overline{9}, - 31.2\overline{9}, - 31.1\overline{9}, - 31.0\overline{9}, - 31, - 30.8\overline{9}, - 30.7\overline{9}, - 30.4\overline{9}, - 30.1\overline{9}, - 30.0\overline{9}, - 30, - 29.8\overline{9}, - 29.7\overline{9}, - 29.6\overline{9}, - 29.5\overline{9}, - 29.4\overline{9}, - 29.3\overline{9}, - 29.2\overline{9}, - 29.1\overline{9}, - 29.0\overline{9}, - 28.7\overline{9}, - 28.6\overline{9}, - 28.5\overline{9}, - 28.4\overline{9}, - 28.3\overline{9}, - 28.2\overline{9}, - 28.1\overline{9}, - 28.0\overline{9}, - 28, - 27.8\overline{9}, - 27.7\overline{9}, - 27.6\overline{9}, - 27.3\overline{9}, - 27.2\overline{9}, - 27.1\overline{9}, - 27.0\overline{9}, - 27, - 26.8\overline{9}, - 26.7\overline{9}, - 26.6\overline{9}, - 26.5\overline{9}, - 26.4\overline{9}, - 26.3\overline{9}, - 26.2\overline{9}, - 26.1\overline{9}, - 26.0\overline{9}, - 26, - 25.8\overline{9}, - 25.7\overline{9}, - 25.6\overline{9}, - 25.3\overline{9}, - 25.2\overline{9}, - 25.1\overline{9}, - 25.0\overline{9}, - 25, - 24.8\overline{9}, - 24.7\overline{9}, - 24.6\overline{9}, - 24.5\overline{9}, - 24.2\overline{9}, - 24.1\overline{9}, - 24.0\overline{9}, - 24, - 23.8\overline{9}, - 23.7\overline{9}, - 23.6\overline{9}, - 23.5\overline{9}, - 23.4\overline{9}, - 23.3\overline{9}, - 23.2\overline{9}, - 23.1\overline{9}, - 23.0\overline{9}, - 23, - 22.8\overline{9}, - 22.5\overline{9}, - 22.4\overline{9}, - 22.3\overline{9}, - 22.2\overline{9}, - 22.1\overline{9}, - 22.0\overline{9}, - 22, - 21.8\overline{9}, - 21.7\overline{9}, - 21.4\overline{9}, - 21.1\overline{9}, - 21.0\overline{9}, - 21, - 20.8\overline{9}, - 20.7\overline{9}, - 20.6\overline{9}, - 20.5\overline{9}, - 20.4\overline{9}, - 20.3\overline{9}, - 20.2\overline{9}, - 20.1\overline{9}, - 20.0\overline{9}, - 20, - 19.8\overline{9}, - 19.7\overline{9}, - 19.6\overline{9}, - 19.5\overline{9}, - 19.4\overline{9}, - 19.1\overline{9}, - 19.0\overline{9}, - 19, - 18.8\overline{9}, - 18.7\overline{9}, - 18.6\overline{9}, - 18.5\overline{9}, - 18.4\overline{9}, - 18.3\overline{9}, - 18.2\overline{9}, - 18.1\overline{9}, - 18.0\overline{9}, - 18, - 17.8\overline{9}, - 17.7\overline{9}, - 17.6\overline{9}, - 17.5\overline{9}, - 17 \frac{1}{2}, - 17.3\overline{9}, - 17.2\overline{9}, - 17.1\overline{9}, - 17.0\overline{9}, - 17, - 16.8\overline{9}, - 16.7\overline{9}, - 16.6\overline{9}, - 16.5\overline{9}, - 16 \frac{1}{2}, - 16.3\overline{9}, - 16.2\overline{9}, - 16.1\overline{9}, - 16.0\overline{9}, - 16, - 15.8\overline{9}, - 15.6\overline{9}, - 15.5\overline{9}, - 15 \frac{1}{2}, - 15.3\overline{9}, - 15.0\overline{9}, - 15, - 14.7\overline{9}, - 14.6\overline{9}, - 14.5\overline{9}, - 14.2\overline{9}, - 14.1\overline{9}, - 14.0\overline{9}, - 14, - 13.8\overline{9}, - 13.7\overline{9}, - 13.6\overline{9}, - 13 \frac{1}{2}, - 13.3\overline{9}, - 13.2\overline{9}, - 13.1\overline{9}$

Step 4